[EM] Approval Voting vs Instant Runoff Voting:

[MIKE OSSIPOFF]

>Martin Harper wrote:
>
> > Right - and I can't see any case where saying you will vote A not AB
> > will cause B voters to vote AB. I'm sure such a case exists - but I
> > can't find it: hence my question at the end: can you provide one?

>


Only if there's no reason to believe that A or B is more rightfully
a compromise. Maybe one seems likely to be bigger, or more of a
middle compromise. If so, that candidate's supporters shouldn't
vote for the other, if ther's any possibility of defection by the other's 
supporters. They should be suspicious of polling results
that surprisingly show the other candidate to be bigger.

But if it really looks, before the poll, as if A & B are equal,
and neither is more middle than the other, then the A voters
have some incentive to bullet-vote in the poll, even if they
wouldn't in the election, hoping they can fool the B voters into
believing that A is bigger.

But, as I said earlier, this is a rare special scenario. Normally it
should be clear who's the compromise. The supporters of a middle
candiate aren't going to vote for an extreme candidate as a
compromise. Gore voters won't vote for Nader as a compromise
(assuming that there was really someone who liked Gore better than
Nader). A Nader voter would have little incentive to falsly bullet vote inIf 
he plans to vote for Gore in the election, he doesn't
have much or anything to gain by bullet voting in the poll.
In fact, he doesn't want to make it look like Gore can't win. He
wants to do what he can to make Gore beat Bush, and that doesn't include 
under-representing Gore's votegetting power. Obvioulsy, he still votes for 
Nader too.

So if we assume it's that kind of an election, where the voters'
poll votes can be trusted, and that the poll is conducted by an
organization trusted by the A voters, then we can trust the polling data in 
Craig's example.

To really know the best way to vote, I'd suggest calculating the Pij.
But Craig was wrong to say that the voters can't maximize their utility 
expectation. They can, by calculating strategic values, based
on the calculated Pij. Vote for everyone whose strategic value is positive.

But he would also be wrong if he claimed that voters who aren't using
mathematical strategy can't maximize their expectation.  If you merely vote 
in the way that you _guess_ is best, in terms of the outcome of the present 
election, then you're genuinely maximizing your expectation. Just as surely 
as if you'd calculated strategy based on estimated Pij.

Morgenstern & von Neuman suggested a way of determining utilities
based on judging how you feel like choosing among lotteries, or among a 
lottery & a definite outcome. With simple lottery situations,if
you know the probabilities, you can calculate what your utilities musts be, 
based on your intuitive choices.

It's assumed that they way you feel like choosing maximizes something,
and the vNM utilities that you calculate from your choice aree what you've 
maximized expectation of.

But what if you don't even know the probabilities numerically? Then
you can't calculate the vNM utilities, but by the same assumptions,
when you do what sems best, you're maximizing your expectation in the best 
way you can.

That's still true if, instead of a simple lottery, it's something more 
complicated, like an election.

That's why I disagree with Craig's statement that voters in his Approval 
example aren't mximizing their expectatgion. If there are vNM utilities that 
you can calculate from your choices in a simple lottery situation, where the 
probabilities are known numerically, because it's assumed that when you use 
your best judgement you're maximizing them,
then aren't you sitll maximizing them when you still use your best
judgement when numerical probabilities aren't available, and it's a more 
complicated situatin, like an election?

I'd only vote for A, for several reasons. For one thing, that's
the way I'm used to voting. A is so much better than the others, that I 
wouldn't even consider strategy. But if I did consider strategy,
intuitively, I'd still vote for A only. Because it feels like the
best strategy, and because I suspect that when the Pij are available,
voting only for A will be the best mathematical strategy.

Mike Ossipoff

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